(1)/(1-√(2) )

Question

`(1)/(1-√(2) )`

Answer 1

`-2.414`

Explanation:

`\sf(1)/(1-√(2) )`

Rationalize the denominator.

For that, multiply both the numerator and denominator by the conjugate of the denominator.

`\sf(1*(1+√(2) ))/((1-√(2))* (1+√(2) ))`

`\sf((1+√(2) ))/(1(1+√(2) )-√(2)(1+√(2) ) )\\\\\sf((1+√(2) ))/(1+√(2) -√(2)-2 )\\\\\sf((1+√(2) ))/(1-2 )\\\\\sf((1+√(2)) )/(-1 )\\\\\sf-1-√(2)`

`-2.414`